Between what two consecutive integers does the largest root of 5x^2+2=-11x lie

We rewrite the expression:
 5x ^ 2 + 2 = -11x
 5x ^ 2 + 11x + 2 = 0
 We use the resolver:
 x = (-b +/- root (b ^ 2 - 4 * a * c)) / (2 * a)
 Substituting values:
 x = (-11 +/- root ((11) ^ 2 - 4 * (5) * (2))) / (2 * (5))
 x = (-11 +/- root (81) / (10)
 x = (-11 +/- 9) / (10)
 The roots are:
 x1 = (-11 + 9) / (10) = -2/10 = -1/5
 x2 = (-11 - 9) / (10) = -20/10 = -2
 The major root is:
 x1 = -1/5 = -0.2
 Which is between the integers:
 -1 and 0
 
 the largest root of 5x ^ 2 + 2 = -11x lies between: 
 -1 and 0